Party is losing 'important segments of the electorate,' former secretary of State says.

Former Secretary of State Condoleezza Rice is the latest Republican to recommend changes to the party, saying on Friday that the GOP needs to appeal to a broader portion of the electorate moving forward.

Rice said on CBS’ This Morning that many key GOP issues are broadly popular -- fiscal responsibility and a strong national defense, for instance -- but the party is losing “important segments of the electorate” because it has not adjusted to changing demographics.

“The changing demographics in the country really necessitates an even bigger tent for the Republican Party,” Rice said. “What we have to do is appeal to those people not as identity groups, but understanding that if you can get the identity issue out of the way then you can appeal on the broader issues that all Americans share concerns for.”

Rice said that on the issues of immigration and women, “some mixed messages” were sent to the electorate, presumably referring to several controversial statements on rape and abortion made by Republican candidates during the campaign. She added that, “When you send mixed messages through the narrow funnel that is the media spotlight, sometimes people hear only one side.”

On the questions surrounding the Obama administration's response to the terrorist attack in Libya, Rice was diplomatic, saying that “shifting stories” sometimes happen on intelligence issues because “you’re getting different sources of information." She added that the accountability review board and congressional intelligence committees will decide whether the administration was at fault.

Rice repeated her position that, if asked, she would not accept the position as Secretary of State in Obama’s second administration.

“I’m going to support my president, but I’m going to stay at Stanford,” she said. “I've had my time.”